GAZA CITY — Israeli military units and Palestinian militants traded fresh attacks Sunday, even as each side offered truces to temporarily halt the bloodshed ahead of the upcoming Muslim holiday.

Each blamed the other for the prolonged fighting.

After initially rejecting an Israeli offer Saturday for a 24-hour truce, Hamas said Sunday it agreed to hold fire ahead of the Eid al-Fitr holiday marking the end of the Muslim fasting month of Ramadan.

But as Israel's Cabinet considered the offer, rockets fell on southern Israel and Israeli strikes could be heard in Gaza.

Hamas said that "due to the lack of commitment" by Israel, it resumed its fire. Israeli Prime Minister Benjamin Netanyahu said that Hamas showed it could not be trusted.

"Israel is not obliged and is not going to let a terrorist organization decide when it's convenient to fire at our cities, at our people, and when it's not," Netanyahu said on Fox News Sunday.

President Obama urged a "humanitarian ceasefire" during a phone call with Netanyahu.

"The president underscored the enduring importance of ensuring Israel's security, protecting civilians, alleviating Gaza's humanitarian crisis, and enacting a sustainable cease-fire that both allows Palestinians in Gaza to lead normal lives and addresses Gaza's long-term development and economic needs, while strengthening the Palestinian Authority," a White House statement said

Hamas' announcement came after Israel offered a 24-truce that was rejected by the militant group late Saturday.

The Israeli military charged that about a dozen rockets were launched from Gaza since midnight, and said it was resuming its military operations in the Gaza Strip as a result.

After Hamas' call for a cease-fire, an Israeli airstrike killed one in Gaza after it hit a vehicle carrying workers who were on their way to fix water pipes, the Palestinian Red Crescent said. At the same time, a rocket fired from Gaza lightly injured one person in Israel, police said, as sirens wailed throughout southern Israel.

The 20-day conflict has left more than 1,030 Palestinians dead, according to the Palestinian Health Ministry in Gaza. In Israel, 46 have died, including 43 soldiers, two civilians and a Thai worker, the Israeli military said.

Palestinians celebrate the announcement of a cease-fire on Aug. 26 in Gaza City. Palestinian President Mahmoud Abbas announced an Egyptian-brokered cease-fire proposal to end seven weeks of fighting between Israel and militant groups in the Gaza Strip. (Photo: Mohammed Saber, European Pressphoto Agency)

A worker removes debris from the Cohen family bedroom after a missile fired by militants in the Gaza Strip made a direct hit in their home in Ashkelon, Israel. (Photo: Abir Sultan, European Pressphoto Agency)

A Palestinian boy walks across the rubble of a house belonging to the al-Dakhani family after an Israeli airstrike on the Rafah refugee camp, southern Gaza Strip. Two people were wounded in the attack. (Photo: Eyad Baba, AP)

A man looks out the window of a damaged classroom after a rocket, fired by Palestinian militants from the Gaza Strip, landed in the courtyard of a kindergarten in Ashdod, Israel. (Photo: Jack Guez, AFP/Getty Images)

A Palestinian man sweeps the floor of his home that was damaged after a mosque across the street was hit by an Israeli airstrike in Beit Lahia in the northern Gaza Strip. (Photo: Roberto Schmidt, AFP/Getty Images)

A Palestinian woman watches from a hole in a home belonging to Hamas financial official Mohammed al-Ghul after it was targeted by an Israeli airstrike in Gaza City. One of several targeted airstrikes by Israeli forces killed Al-Ghul in his vehicle. (Photo: Mohammed Abed, AFP/Getty Images)

Relatives and close family friends of Daniel Turgeman touch his coffin during the boy's funeral on Aug. 24 in Yevul, Israel. Turgeman, 4, was killed in a mortar attack fired by Palestinians inside the Gaza Strip on Aug. 22. (Photo: Jim Hollander, European Pressphoto Agency)

An Israeli firefighter extinguishes a fire after rockets fired by Palestinian militants from the Gaza Strip hit a field near the southern Israeli city of Sderot. (Photo: Menahem Kahana, AFP/Getty Images)

Palestinians carry the body of the wife of Mohammed Deif, Israel's most-wanted man, at the Jabaliya refugee camp in the northern Gaza Strip. According to media reports, Deif's wife and son were killed Aug. 20 in an Israeli airstrike on Gaza City. Israel holds Deif, the leader of the Qassam Brigades, Hamas' military wing, accountable for directing the Gaza conflict from underground. (Photo: Mohammed Saber, European Pressphoto Agency)

Israeli soldiers in an undisclosed southern Israeli location take cover inside a cement pipe near the border with the Gaza Strip as a 'red alert' sounds, signaling that Palestinian militants have fired a rocket toward the area. The Israeli army reported that Palestinians shot about 180 rockets and mortars since the collapse of the cease-fire, with scores of Israeli strikes inside the Gaza Strip. (Photo: Avi Roccah, European Pressphoto Agency)

Palestinians grieve over the death of Widad Mustafa Deif, 27, and her 8-month-old son, Ali Mohammed Deif, during their funeral in Jabaliya refugee camp. They were killed by an Israeli strike Aug. 20. (Photo: Khalil Hamra, AP)

A Palestinian boy spots two Israeli drones in the late afternoon Aug. 19. Palestinians fled their homes in neighborhoods of eastern Gaza City carrying bags of clothes, pillows and mattresses after renewed Israeli airstrikes, witnesses said. Nine days of relative quiet in the skies over Gaza came to an abrupt halt when rockets struck Israel just hours before the truce was to expire at midnight local time. Israel immediately ordered a military response, with warplanes striking targets across the coastal strip. (Photo: Roberto Schmidt, AFP/Getty Images)

A rocket fired by Palestinian militants inside the Gaza Strip rises into the night sky. More than 50 rockets were fired toward Israeli civilian centers from Gaza on Aug. 19, shattering the 24-hour cease-fire, and Israel responded with multiple air force attacks on Gaza, with deaths and many casualties reported. (Photo: Avi Roccah, European Pressphoto Agency)

Palestinian rescuers clear the rubble of a destroyed house following an Israeli airstrike in Gaza City. The Israeli airstrike killed a young girl and a woman, wounding 16 other people. (Photo: Mohammed Abed, AFP/Getty Images)

An Egyptian soldier stands guard on the Egyptian side of the border between Egypt and the Gaza Strip on Aug. 13, overlooking the damage in Rafah caused by a month of fighting between the Israeli military and Hamas militants. (Photo: Said Khatib, AFP/Getty Images)

Palestinian mourners carry the body of Zakariah al-Aqrah, 21, during his funeral in the West Bank village of Qabalan. The Israeli military said it killed al-Aqrah early Monday morning after he opened fire on an Israeli force that had come to arrest him in connection with shootings targeting Israeli soldiers two weeks ago. (Photo: Majdi Mohammed, AP)

A Palestinian man standing in a crowd of onlookers reacts to watching a soap factory go up in flames moments after it was hit by an Israeli airstrike in Gaza City, Aug, 10. (Photo: Roberto Schmidt, AFP/Getty Images)

Speaking to CNN, he added Palestinian President Mahmoud Abbas is forming a delegation to go to Cairo to work on negotiating a cease-fire.

"Israel has a hidden agenda: To really destroy and totally destroy the Palestinian reconciliation'' that led to formation of Palestinian Authority government, Shtayyeh said.

Saturday's 12-hour truce allowed Palestinians to move medical supplies and tend to the dead and injured in the Gaza Strip. Gazans found dozens of bodies buried under rubble of buildings demolished by airstrikes and shelling.

In Gaza, many say the high death toll belies any attempt by Israel to minimize civilian casualties.

"I wonder how Israeli mothers feel when they see our children killed, our homes attacked — do they really have hearts or do they just consider us animals," asked Um Ateyya, 57, a grandmother in Gaza City.

International efforts to secure a lasting cease-fire have so far failed. On Friday, Israel rejected a week-long truce because officials said it was would force them to interrupt their operations to destroy the tunnels it deems a strategic threat because they allow Hamas fighters to attack Israel.

A truce proposed by Egypt two weeks ago was rejected by Hamas because the group said it wasn't consulted. Hamas refuses to agree to any cease-fire that doesn't include the lifting of a blockade surrounding Gaza that has been in place since 2007.

Ahead of the announcement of the holiday cease-fire, Zuhri said any truce must include a withdrawal of Israeli forces from Gaza, and that tens of thousands of displaced people must be allowed to return to their homes.

Israel's current terms are "not acceptable," he said in a text message to journalists.

Israel and Hamas, a U.S.-designated terrorist group that governs the Gaza Strip, have fought at least 10 wars and skirmishes in the past decade. The latest round of Gaza fighting began July 8 and with the collapse of truce talks in Cairo, there's risk of protracted fighting. A look at events since the collapse of the talks on August 19.